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Characterization of large energy solutions of the equivariant wave map problem: I
We consider $1$-equivariant wave maps from ${\Bbb R}^{1+2}\to{\Bbb S}^2$. For wave maps of topological degree zero we prove global existence and scattering for energies below twice the energy of
Stability of stationary equivariant wave maps from the hyperbolic plane
In this paper we initiate the study of equivariant wave maps from $2d$ hyperbolic space, ${\Bbb H}^2$, into rotationally symmetric surfaces. This problem exhibits markedly different phenomena than
Scattering for the radial 3D cubic wave equation
Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in $\dot{H}^{\frac{1}{2}} \times
The Cauchy problem for wave maps on a curved background
We consider the Cauchy problem for wave maps $${u: {\mathbb R}\times M \to N,}$$ for Riemannian manifolds (M, g) and (N, h). We prove global existence and uniqueness for initial data, u[0] = (u0,
Profiles for the Radial Focusing 4d Energy-Critical Wave Equation
Consider a finite energy radial solution to the focusing energy critical semilinear wave equation in 1 + 4 dimensions. Assume that this solution exhibits type-II behavior, by which we mean that the
The Cauchy problem for wave maps on hyperbolic space in dimensions $d \geq 4$
We establish global well-posedness and scattering for wave maps from $d$-dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small in the critical
Relaxation of Wave Maps Exterior to a Ball to Harmonic Maps for All Data
In this paper we establish relaxation of an arbitrary 1-equivariant wave map from $${\mathbb{R}^{1+3}_{t,x}{\setminus} (\mathbb{R}\times B(0,1))\to S^3}$$Rt,x1+3\(R×B(0,1))→S3 of finite energy and
Scattering for Radial, Semi-Linear, Super-Critical Wave Equations with Bounded Critical Norm
In this paper we study the focusing cubic wave equation in 1 + 5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target
Equivariant Wave Maps on the Hyperbolic Plane with Large Energy
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is the hyperbolic plane
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